Date & Time: Wednesday, July 1, 2015, 16:00-17:00.
Venue: Ramanujan Hall

Speaker: M. Ram Murty, Queens University

Title: Consecutive squarefull numbers

Abstract: A natural number is called squarefull if whenever a prime p divides it, so does p^2. Erdos conjectured that the number of squarefull numbers less than x is bounded by (log x)^A for some A positive. We will prove this conjecture assuming the ABC conjecture and also obtain some unconditional results. We also relate this problem to the study of fundamental units in real quadratic fields. This is joint work with Kevser Aktas.